Coleman integration for hyperelliptic curves : algorithms and applications
Name
767738207-MIT.pdf
Description
Full printable version
Size
8.58 MB
Format
Adobe PDF
Checksum (MD5)
c6d3c59904552d965f4bf6d880bb8ab3
Author(s)
Balakrishnan, Jennifer Sayaka (Jennifer Shyamala Sayaka)
Advisor(s)
Kiran S. Kedlaya.
Date Issued
2011
Publisher
Massachusetts Institute of Technology
Abstract
The Colemani integral is a p-adice line integral that can be used to encapsulate several quantities relevant, to a study of the arithmetic of varieties. In this thesis, I describe algorithms for computing Coleman integrals on hyperelliptic curves and discuss some immediate applications. I give algorithms to compute single and iterated integrals on odd models of hyperelliptic curves, as well as the necessary modifications to iplemieit these algorithms for even models. Furthermore, I show how these algorithinis can be used in various situations. The first application is the method of Chabatv to find rational points on curves of genus greater than 1. The second is Mlihyong Kim's recent nonabelian analogue of the Chabauty method for elliptic curves. The last two applications concern p-adic heights on Jacobians of hyperelliptic curves. necessary to formulate a p-adic analogue of the Birch and Swinnerton-Dyer conjecture. I conclude by stating the analogue of the Mazur-Tate-Teitelbaum conjecture iii our setting and presenting supporting data.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 171-175).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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